Rút gọn các biểu thức sau:
a) \((a + b)^2 – (a – b)^2\); b) \((a + b)^3 – (a – b)^3 – 2b^3 \)
c) \((x + y + z)^2 – 2(x + y + z)(x + y) + (x + y)^2\)
\(a) (a + b)^2 – (a – b)^2 = (a^2 + 2ab + b^2) – (a^2 – 2ab + b^2)\)
\( = a^2 + 2ab + b^2 – a^2 + 2ab - b^2 = 4ab\)
\(b) (a + b)^3 – (a – b)^3 – 2b^3 = (a^3 + 3a^2b + 3ab^2 + b^3) – (a^3 – 3a^2b + 3ab^2 – b^3) – 2b^3\)
\(= a^3 + 3a^2b + 3ab^2 + b^3 – a^3 + 3a^2b - 3ab^2 + b^3 – 2b^3 = 6a^2b\)
\(c) (x + y + z)^2 – 2(x + y + z)(x + y) + (x + y)^2\)
\(=[(x+y+z)-(x+y)]^2 =(x+y+z-x-y)^2=z^2\)
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